The carbon tax is a tax on CO2 emissions. It aligns incentives of business (profit) and society (stable climate) by giving businesses an opportunity to make more money if they find ways to reduce their CO2 emissions.
One open question with the carbon tax is how to choose the tax rate. Several countries already have a carbon tax, but they seem to set it at a fixed rate, or increase it by a fixed amount each year. Even the Carbon Tax Center says, “There is no magic formula or right number”. I think they're approaching it wrong. Carbon taxes are essentially prices on carbon emissions. Governments shouldn't set prices, and they shouldn't set carbon tax rates either. The market should do it, with a little help from the government.
First, we should decide what level of CO2 emissions are “sustainable”. You can think of this as the “supply” of available emissions. There is no need to go below this level, although doing so will not be harmful. We should be able to continue emitting at the sustainable level for thousands of years. This level is then set as the eventual sustainable target.
Our current emissions are rather high. We can think of this as “demand”. Since demand is higher than supply, we need to raise prices (the carbon tax rate, currently 0% in the U.S.). We need to decide when we want to reach the sustainable level, and then interpolate target levels from the current level to the sustainable target. This might be a straight line for simplicity, but could also be an S-curve or exponential decay.
For example, let's say that the current CO2 emissions are 6 billion metric tons, and we decide that 1 billion metric tons, combined with more forests, is sustainable. Let's further suppose that we want to reach this target in 10 years. That means we need to reduce emissions by 0.5 billion metric tons each year, so we set our target for 2009 to 5.5, 2010 to 5.0, 2011 to 4.5, etc., until 2018, at 1.0 billion metric tons.
Each year (or perhaps every month), we look at the current level of emissions and the target level, and increase or decrease the carbon tax rate. If we're emitting more than the target, we'll increase the tax rate. If we're emitting less (which may happen in a few years, if all the businesses are competing to increase profits by reducing emissions), then we decrease the tax rate. By altering the tax rate in this way, we can stay close to the target.
The problem on the business side is that if the tax rates change every month, there's a lot of uncertainty (just as for any prices that change suddenly every month), and it's hard to change plans that quickly. What will likely develop is an insurance market. Insurers will sell insurance that the tax rate won't go up much, and businesses will buy the insurance to hedge against sudden increases. Does this eliminate the incentives for businesses? No! They're now paying insurance and taxes. The cost of insurance is set by the likelihood at the tax rates will go up. The insurance industry is in the best position to guess this, because they'll be visiting the businesses to determine how quickly emission reductions are going into place. The insurance companies will then be able to predict the future emissions, and set insurance rates based on that. Since they're the ones making payouts when businesses (collectively) don't reduce emissions, the insurance companies will then have an incentive to push businesses to act sooner. They also have the incentive to share techniques across businesses. They make more money when businesses collectively reduce emissions.
Most carbon tax proposals use a fixed price and hope that the output will decline. Most cap-and-trade proposals use a hard limit on emissions, and a variable, potentially volatile price. The variable carbon tax rate proposal combines aspects of both approaches. It uses variable prices, but they're varying less often; it uses a target instead of a hard cap, which allows businesses to buy more time; and it generates revenue for society. With a market based scheme, incentive are aligned. Society will want reduced emissions, businesses will want to reduce tax rates (by reducing emissions), and insurance companies will want to reduce payouts (by convincing businesses to reduce emissions). If businesses fail to reduce emissions, they pay an ever increasing compensation to society for the delay. Furthermore, the open question of what to set the tax to, which is open to lobbying, is replaced by the question of how much to change the tax, which I think is harder to game. This scheme also tells you when we've achieved our goal: emissions are at the sustainable target level. Even at this level, we continue the carbon tax to prevent emissions from going up, and we continue to take in revenue from those businesses that produce emissions. This will keep our emissions near the sustainable level.